Page 401 - Color_Atlas_of_Physiology_5th_Ed._-_A._Despopoulos_2003

Important Equations in Physiology
1. Fick’s law of diffusion for membrane trans- 4. Nernst equation (see also p. 32)
port (see also p. 20ff.) –1 · log [X] i [mV]
∆C E x = –61 · z x
J diff = F · D · [mol · s ] [X] a
–1
∆x E x = equilibrium potential of ion X [mV];
–1
J diff = net diffusion rate [mol · s ]; z x = valency of ion X;
2
A = area [m ]; [X] i = intracellular concentration of ion X
D = diffusion coefficient [m · s ]; [mol · m ]
2
–1
–3
∆C = concentration difference [mol · m ]; [X o] = extracellular concentration of ion X
–3
–3
∆x = membrane thickness [m] [mol · m ].
Alternative 1:
5. Ohm’s Law (see also pp. 32, 188)
J diff = P · ∆C [mol · m –2 · s ]
–1
F a. For ion transport at membrane
–1
P = permeability coefficient [m · s ]; I x = g x · (E m –E x) [A · m ]
–2
J diff, A an ∆C; see above
I x = ionic current of ion X per unit area
Alternative 2 (for gas diffusion) of membrane [A · m ];
–2
.
Appendix V diff = net diffusion rate [m · s ]; [S · m ];
∆P
g x = conductance of membrane to ion X
[m · s ]
–1
V diff
= K ·
∆x
F
–2
.
3
–1
E m = membrane potential [V];
-1
2
-1
13 K = Krogh’s diffusion coefficient [m · s · Pa ] E x = equilibrium potential of ion X [V]
∆P = partial pressure difference [Pa]
b. For blood flow:
.
2. Van’t Hoff–Stavermann equation Q = ∆P [L · min ]
–1
(see also p. 377) . R
Q = flow rate (total circulation:
∆π = σ · R · T · ∆c osm [Pa] cardiac output, CO) [L · min ]
–1
∆π = osmotic pressure difference [Pa] ∆P = mean blood pressure difference
σ = reflection coefficient [dimensionsless] (systemic circulation: P aorta –P vena cava;
R = universal gas constant [8.3144J · K –1 · lesser circulation: P pulmonary artery –P pulmo-
mol ]; nary vein) [mmHg]
–1
T = absolute temperature [K]; R = flow resistance (systemic circula-
∆c osm = concentration difference of tion:
–3
osmotically active particles [mol · m ]. total peripheral resistance = TPR)
[mmHg · min · L ].
–1
3. Michaelis-Menten equation
(see also pp. 28, 383ff.) 6. Respiration-related equations
C (see also pp. 106, 120)
–1
J sat = J max · [mol · m –2 · s ],
K M + C a. Tidal volume (V T):
J sat = substrate transport (turnover) V T = V D + V A [L]
–1
[mol · m –2 · s ]; b. Respiratory volume per minute
.
.
J max = maximum substrate transport (V E oder V T):
.
(turnover) [mol · m –2 · s ]; V E = f · V T = (f · V D) + (f · V A) =
–1
.
.
–3
C = substrate concentration [mol · m ]; V D + V A [L · min ]
–l
K M = Michaelis constant = substrate c. O 2 consumption, CO 2 emission,
concentration at /2 J max [mol · m ]. and RQ (total body:)
–3
1
.
.
V O 2 = V T (FI O 2 –FE O 2 ) = CO · avD O 2 [L · min ]
–1
.
.
–1
V CO 2 = V T · FE CO 2 [L · min ]
.
.
RQ = V CO 2
388 V O 2
Despopoulos, Color Atlas of Physiology © 2003 Thieme
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